It does sound like you are working remotely for the convenience of the employer. So (roughly) 4/5 of your income is NJ source income, and 1/5 is NY source income, for the time that you actually work physically in NY. When you prepare your NY nonresident tax return you will be asked how much of your income should be allocated to NY. You can do the allocation based on the number of days. So NY will tax only the NY source income. Ideally you should keep a record of the days that you actually work in each state.
When you prepare your tax returns, do the New York nonresident tax return first, then the NJ resident tax return, to make sure that the NJ credit is calculated correctly for the tax that you pay to NY.
If your employer can withhold tax for both states, that will be helpful, so you will not have to make estimated tax payments to either state. You will be paying most of your tax to New Jersey.
